Relationships Between Quantities

The cost, c, of a ham sandwich at a deli varies directly with the number of sandwiches, n. If c = $54 when n is 9, what is the cost of the sandwiches when n is 3? A) $18 B) $21 C) $27 D) $48

A) $18

If u(x) = x^5 - x^4 + x^2 and v(x) = -x^2, which expression is equivalent to (U/V) (X)? A) x^3 - x^2 B) -x^3 + x^2 C) -x^3 + x^2 - 1 D) x^3 - x^2 + 1

C) -x^3 + x^2 - 1

Which algebraic expression represents the phrase "seven more than half of a number"? A) 7 - 1/2x B) -7 + 1/2x C) 1/2x + 7 D) -1/2x -7

C) 1/2x + 7

Each week, Rosario drives to an ice-skating rink that is 60 miles away. The round-trip takes 2.75 hours. If he averages 55 miles per hour on his way to the rink, which equation can be used to find x, the number of miles per hour he averages on his way home? A) 60/55 + 60/x = 2.75 B) (60/55) (60/x) = 2.75 C) 60(55) + 60x = 2.75 D) [60(55)] (60x) = 2.75

A) 60/55 + 60/x = 2.75

Which function has an inverse that is also a function? A) g(x) = 2x - 3 B) k(x) = -9x2 C) f(x) = |x + 2| D) w(x) = -20

A) g(x) = 2x - 3

Which of the following is an even function? A) g(x) = (x - 1)^2 + 1 B) g(x) = 2x^2 + 1 C) g(x) = 4x + 2 D) g(x) = 2x

B) g(x) = 2x^2 + 1

The value, V(m), of a comic book m months after publication has an average rate of change of -0.04 between m = 36 and m = 60. Which statement must be true? A) The value of the comic book decreased by a total of $0.04 between m = 36 and m = 60. B) The value of the comic book increased by a total of $0.04 between m = 36 and m = 60. C) The value of the comic book decreased by an average of $0.04 each month between m = 36 and m = 60. D) The value of the comic book increased by an average of $0.04 each month between m = 36 and m = 60.

C) The value of the comic book decreased by an average of $0.04 each month between m = 36 and m = 60.

Which property of real numbers is shown below? 3 + ((-5) + 6) = (3 + (-5)) + 6 A) commutative property of addition B) identity property of multiplication C) associative property of addition D) commutative property of multiplication

C) associative property of addition

Which phrase represents the algebraic expression 5x - 9? A) the product of five times a number and nine B) the difference of nine times a number and five C) the sum of five times a number and five D) the difference of five times a number and nine

D) the difference of five times a number and nine

If a(x) = 2x - 4 and b(x) = x + 2, which of the following expressions produces a quadratic function? A) (ab)(x) B) (a/b) (x) C) (a - b)(x) D) (a + b)(x)

A) (ab)(x)

If s(x) = 2 - x2 and t(x) = 3x, which value is equivalent to (s*t) (-7)? A) -439 B) -141 C) 153 D) 443

A) -439

Given f(x)=17-x^2, what is the average rate of change in f(x) over the interval [1, 5]? A) -6 B) -1/2 C) 1/4 D) 1

A) -6

If f(x) is an even function and (6, 8) is one the points on the graph of f(x), which reason explains why (-6, 8) must also be a point on the graph? A) Since the function is even, the outputs of a negative x-value and a positive x-value are the same. B) Since the function is even, the outputs of a negative y-value and a positive y-value are the same. C) The graph has rotational symmetry, so the point will be reflected across the y-axis. D) The graph has rotational symmetry, so the point will be rotated 90 degrees about the origin.

A) Since the function is even, the outputs of a negative x-value and a positive x-value are the same.

Paul can install a 300-square-foot hardwood floor in 18 hours. Matt can install the same floor in 22 hours. How long would it take Paul and Matt to install the floor working together? A) 4 hours B) 9.9 hours C) 13.2 hours D) 30 hours

B) 9.9 hours

To determine whether a graph of a relation is also a function, Shayla declares that the y-axis is a vertical line and counts the number of times that the graph intersects the y-axis. If the graph has exactly one y-intercept, Shayla concludes that the graph shows a function. In all other cases, she declares that it is not a function. Is Shayla applying the vertical line test correctly? A) No, because the y-axis is a horizontal line. B) No, because using the y-axis tests only whether x = 0 is mapped to multiple values. C) Yes, because multiple y-intercepts represent multiple x-values being mapped to y = 0. D) Yes, because the y-axis represents all vertical lines of the x-values.

B) No, because using the y-axis tests only whether x = 0 is mapped to multiple values.

Two-fifths of one less than a number is less than three-fifths of one more than that number. What numbers are in the solution set of this problem? A) x < -5 B) x > -5 C) x > -1 D) x < -1

B) x > -5

If h(x) is the inverse of f(x), what is the value of h(f(x))? A) 0 B) 1 C) x D) f(x)

C) x

Eight less than four times a number is less than 56. What are the possible values of that number? A) x > 12 B) x < 12 C) x < 16 D) x > 16

C) x < 16

If f(x)=7+4x and g(x)=1/2x, what is the value of (f/g) (5)? A) 11/2 B) 27/10 C) 160 D) 270

D) 270

If c(x) = 4x - 2 and d(x) = x^2 + 5x, what is (c*d) (x)? A) 4x^3 + 18x^2 - 10x B) x^2 + 9x - 2 C) 16x^2 + 4x - 6 D) 4x^2 + 20x - 2

D) 4x^2 + 20x - 2